Operating turbine resonant blade monitor

ABSTRACT

An operating turbine monitor is described incorporating one or more acoustic sensors positioned next to a blade row of a rotor, an analog digital converter, a tachometer sensor at the rotor shaft, a memory, a synchronous averaging circuit, a subtractor circuit, and a comparator. The invention overcomes the problem of monitoring an operating tubine for order-related turbine blade vibration and for non order-related turbine blade vibration as well as for other turbine conditions.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to monitoring the vibration of turbine blades inan operating turbine and more particularly to detecting and locatingresonantly vibrating turbine blades.

2. Description of the Prior Art

In U.S. Pat. No. 4,422,333 by R. L. Leon, the inventor herein, and whichissued on Dec. 27, 1983, a method and apparatus was described fordetecting and identifying one or more excessively vibrating blades ofthe rotating portion of a turbomachine. An acoustic sensor waspositioned to receive a characteristic Doppler waveform that resultedwhen a blade or blade group vibrates resonately at an order of runningspeed. The method described in the '333 patent for constant speedturbines, involved synchronous averaging out the non order-relatedbackground noise followed by editing or blanking out the few orderrelated components known to be contaminated with background error suchas blade passing frequency and once-per-revolution andtwice-per-revolution frequencies. The resulting signal is then displayedto reveal the characteristic Doppler waveform of the blade vibrations.An envelope detection technique was employed to accurately pick out theamplitude peak indicative of the location of the resonant blade. It wasdiscovered that in some steam power turbines the order relatedbackground error was not limited to just a few order-related components,but instead was spread broadly across all the order related components.Blanking all of the offending order-related background components would,of course, eliminate entirely the sought after Doppler waveform.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method and apparatus isprovided for detecting a resonantly vibrating blade attached to theshaft of a rotating rotor in an operating turbine comprising an acousticsensor positioned on a stationary member with respect to the rotor toreceive sound waves emanating from the vibrating blade of the rotor asthe blade rotates about its rotor axis and to provide an acoustic signalfrom the received sound waves, the acoustic sensor positioned withrespect to the rotor so that the blade approaches and departs from theacoustic sensor in the course of one rotation of the rotor about therotor axis thereby imparting a Doppler effect to the received soundwaves, a sensor for obtaining a reference signal indicative of rotorposition at least once each time the rotor completes a revolution aboutthe rotor axis to provide an indication of angular velocity of the rotorfor each revolution, an analog to digital converter for sampling theacoustic signal to obtain samples during each revolution of a pluralityof revolutions of the rotor including at least some revolutions at afirst and a second angular velocity of the rotor, a circuit or digitalcomputer for averaging the amplitude and taking into account thepolarity of the samples obtained at respective rotor positions withineach revolution of the rotor revolving at the first angular velocity andfor separate averaging the amplitude and taking into account thepolarity of the samples within each revolution of the rotor revolving atthe second angular velocity, a circuit or digital computer forsubtracting the amplitudes and taking into account the polarity ofaveraged samples obtained at respective rotor positions of the rotorrevolving at the first and at the second angular velocity to provide adifference Doppler signal at respective rotor positions of the rotorwhereby order-related background noise due to other blades havingnonuniformity in angular position on the rotor is removed, and a circuitfor comparing the amplitude of the difference Doppler signal atrespective rotor positions of the rotor with a threshold value wherebyan amplitude above the threshold value are indicative of the resonantlyvibrating blade.

The invention further provides a method and apparatus for detecting aresonantly vibrating blade attached to the shaft of a rotating rotor inan operating turbine comprising two acoustic sensors spaced apart fromone another, each positioned on a stationary member with respect to therotor to receive sound waves emanating from the vibrating blade of therotor as the blade rotates about its rotor axis and to provide anacoustic signal from the received sound waves, each acoustic sensorpositioned with respect to the rotor so that the blade approaches anddeparts from the acoustic sensor in the course of one rotation of therotor about the rotor axis thereby imparting a Doppler effect to thereceived sound waves, a sensor for obtaining a reference signalindicative of rotor position at least once each time the rotor completesa revolution about the axis to provide an indication of angular velocityof the rotor for each revolution, a circuit or an analog to digitalconverter for sampling the acoustic signal at each sensor to obtainsamples as a function of rotor position as the rotor makes a pluralityof revolutions at a first and at a second angular velocity of the rotor,a circuit or computer for averaging the amplitude and taking intoaccount the polarity of the samples at respective rotor positions atrespective angular velocities at respective sensors, a circuit orcomputer for subtracting the averaged amplitude and taking into accountthe polarity of samples at respective rotor positions at respectivesensors at said first angular velocity from a corresponding averagedsample at said second angular velocity to form a difference Dopplersample at each sensor at each respective rotor position, a circuit orcomputer for phase shifting or transforming the difference Dopplersamples at one or at each sensor in time to correspond to the samelocation on the rotor at the samples were taken to provide transformeddifference Doppler samples with respect to each sensor, a circuit orcomputer for subtracting amplitude normalized transformed differenceDoppler samples of two sensors from each other corresponding to the samelocation on the rotor to provide a difference difference Doppler sample.

It is the object of the invention to use one acoustic sensor and atleast two angular velocities of a nearly constant speed turbine to forma difference Doppler signal from averaged signals at each angularvelocity.

It is a further object of the invention to use two acoustic sensors andtwo angular velocities to form a first difference Doppler signal fromaveraged signals at each sensor respectively and then to form adifference difference Doppler signal by subtracting the first differenceDoppler signal at the two sensors to uncover low level Doppler waveformsin the presence of a much higher level geometry-sensitive order-relatedbackground waveform. The first difference Doppler signal at one sensormay be shifted in phase by the separation angle between the two sensorsto correspond to the same location on the rotor and normalized inamplitude.

It is a further object of the invention to use a mathematical techniquesuch as a Hilbert Transform to localize the maximum amplitude of thedifference Doppler signal as well as the instantaneous frequency at themaximum amplitude of the difference Doppler signal indicative of thelocation and resonant frequency of the vibrating blade in the operatingturbine.

It is a further object of the invention to utilize synchronous timerecords where each record, consisting, for example, of 64 samples orpoints, would be tagged with a label indicating the exact speed orangular velocity of the rotor shaft at the time of capture. The angularvelocity may be in increments of 0.125 RPM over a range of ±1 RPM for apower turbine operating at 3600 RPM.

It is a further object of the invention to detect non order-related orfluttering turbine blades by processing the data obtained from manyrevolutions with the data obtained from a few revolutions.

It is a further object of the invention to detect non order-relatedaerodynamic events in an operating turbine such as condensation shock orrotating stall by processing the data obtained from one acoustic sensorsensed over many revolutions with the data obtained from one or moreconsecutive revolutions.

It is a further object of the invention to detect differential or unevennozzle wear between two or more nozzle sections in the control stage orfirst stage of a high pressure turbine by positioning a dynamic pressureor acoustic sensor down stream of the rotating blade row downstream,behind each nozzle section and comparing the order-related signal fromthe same rotating blades by synchronous averaging the order-relatedsignals to remove non order-related signals and phase shifting them forcomparison in amplitude to provide an indication of differential nozzlewear.

It is a further object of the invention to detect and measureorder-related resonant torsional shaft vibration which projects out intolarge tangential blade vibration at the blade tips.

It is a further object of the invention to detect order-related resonanttorsional shaft vibration by obtaining the difference Doppler and thendetermining the variation in magnitude as a function of angular positioncf the shaft whereby a sine wave amplitude variation is indicative ofresonant shaft vibration and the number of sine wave cycles within arevolution of the shaft corresponds to the number of orders of thetorsional shaft vibration.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pictorial and schematic diagram of a two flow tandemcompound turbine.

FIG. 2 is a cross section view along the lines 2-2 of FIG. 1.

FIGS. 3 and 4 show one turbine blade of a blade row vibrating at a firstand at a fourth resonant frequency respectively.

FIGS. 5 and 6 show one turbine blade of a blade row vibrating at firstand fourth resonant frequencies shifted in phase respectively.

FIG. 7 is one embodiment of the invention.

FIG. 8 is a first alternate embodiment of the invention.

FIG. 9 is a second alternate embodiment of the invention.

FIG. 10 is a third alternate embodiment of the invention.

FIG. 11 is a fourth alternate embodiment of the invention.

FIG. 12 is a fifth alternate embodiment of the invention.

FIG. 13 is a sixth alternate embodiment of the invention.

FIG. 14 is a seventh alternate embodiment of the invention.

FIG. 15 is an eighth alternate embodiment of the invention.

FIG. 16 is a ninth alternate embodiment of the invention.

FIG. 17 is a graph of a Campbell diagram showing natural bladevibration, frequency and running speed frequencies.

FIG. 18 is a tenth alternate embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1, a pictorial and schematic diagram of a two flowtandem compound turbine 14 is shown. Compound turbine 14, as shown inFIG. 1, has a high pressure turbine 16, an intermediate pressure turbine17 and two low pressure turbines 18 and 19 having a common shaft 20which is cylindrical in shape for receiving and transmitting to a load,for example an electrical generator, torsional load forces and power.Shaft 20 is supported and held in place by bearings 21-24. Bearings21-24 are held in place by suitable support fixture for holding bearings21-24 firmly in place and supporting the weight on shaft 20 as well asshaft 20. Attached or secured to shaft 20 in high pressure turbine 16are blade rows 25-28. Each blade row, for example blade row 25,comprises a plurality of blades, for example, 100, extending radiallyfrom shaft 20. A housing 29 encloses blade rows 25-28 as well asproviding support for turbine nozzles and vanes for controlling anddirecting high pressure steam through high pressure turbine 16.Similarly, intermediate pressure turbine 17 has blade rows 32-35 whichare enclosed by housing 36. Steam from high pressure turbine 16 iscoupled to intermediate pressure turbine 17 by duct 37. Steam fromintermediate pressure turbine 17 is coupled to low pressure turbines 18and 19 by way of duct 38. Low pressure turbine 18 has blade rows 42-47enclosed by housing 54 and has an exhaust duct 55. Low pressure turbine19 has blade rows 48-53 enclosed by housing 56 which has an exhaust duct57. The number of blade rows in turbines 16-19 may vary depending uponthe turbine as well as the number of fixed vanes and inlet nozzles fordistributing and controlling the steam entering and passing through therespective turbine. A high pressure steam source 60 provides highpressure steam, for example, at 1000 degrees centigrade and at 155pounds per square centimeter (1000 pounds per square inch (psi)) whichmay pass over duct 61 into an inlet nozzle not shown within housing 29of turbine 16. The steam passes through turbine 16 over duct 37 throughturbine 17 over duct 38 where it divides. A portion of the steam passesover duct 62 through turbine 18 and out exhaust 55. The other portion ofsteam passes over duct 63 through turbine 19 and out exhaust duct 57.

Compound turbine 14 may operate in a power plant for producingelectricity, for example, 60 hertz or 50 hertz alternating current byway of electrical generator 64. Shaft 20 may have an angular velocity of3600 revolutions per minute or 1800 revolutions per minute (rpm) toproduce 60 hertz alternating current from electrical generator 64.Alternately, shaft 20 may have an angular velocity of 3000 rpm or 1500rpm to produce 50 hertz alternating current from electrical generator64.

The angular velocity of shaft 20 may be determined by a tachometersensor 70 having an output over leads 71 and 72. Tachometer sensor 70may be positioned close to shaft 20 having an optical coupling such asby light to detect each revolution made by shaft 20. Shaft 20 may have astrip of reflective tape thereon or some other suitable means tocommunicate the position of the shaft 20 as it completes a revolution.Tachometer sensor 70 may be supported by the same support fixture thatsupports bearing 21 so that the position of tachometer sensor 70 remainsfixed in relation to longitudinal axis 73 of shaft 20 and of rotor 30.

Referring to FIG. 2, a cross sectional view of high pressure turbine 16is shown to illustrate blade row 25 and two acoustic sensors 76 and 77mounted through housing 29 to be positioned downstream of blade row 25in locations 87 and 130 respectively. As many as 150 blades may be in ablade row. The ends of the blades may be free or they may be attached toa shroud at the end of the blade by means of a tenon passing therethrough and riveted over to form a blade group. Alternately, wires mayextend through the blades to allow movement of the blades relative toone another but to dampen their vibration. FIG. 2 shows, for example,individual blades 78-81 and a blade group 82 of four blades 74, 75, 84and 85 having a shroud 83 attached to the ends of the blades 74, 75, 84and 85.

Acoustic sensors 76 and 77 are positioned with respect to blade row 25so that the individual blades 78-81 or blade group 82 approaches anddeparts from the acoustic sensors 76 and 77 in the course of onerotation of shaft 20 about shaft axis 73 thereby imparting a Dopplereffect to the received sound waves.

As blade row 25 shown in FIG. 2 rotates with shaft 20 as shaft 20rotates (as shown by arrow 69) acoustic sensors 76 and 77 record certainacoustic signals. The acoustic signals are order related which are forthe most part a function of the angular position of blade row 25 andreoccur each revolution of shaft 20. Examples of order-related signalsare 1. blade row nonuniformity i.e. nonuniform blade wake caused by, forexample, uneven spacing of the blades about shaft 20 and blade passingfrequency and 2. an individual resonantly vibrating blade or bladegroup. The blades may be excited into resonance by the nozzle passingfrequency which occurs when a plurality of nozzles discharge steam whichimpact on blade row 25 as blade row 25 is rotating at the operating orrunning speed, or by any integer multiple of running speed due to normalnonuniformities in the spacing between nozzle blades. Acoustic sensors76 and 77 may have a separation angle with respect to the rotation ofshaft 20 of about 9 degrees for good results. Order-related acousticsignals are a function of the rpm of shaft 20 and frequency harmonics ofthe running speed. Non order-related acoustic signals may be due to, forexample, background noise of steam passing through turbine 16 or due tononresonant vibrations of individual blades or blade groups for exampleat the natural vibration frequency of the blade.

FIG. 3 shows an individual blade 78 on shaft 20 without vibration. Blade78' is shown in FIG. 3 having a vibration at the natural frequency ofthe blade.

FIG. 4 shows blade 78 on shaft 20 without vibration. Blade 78'' is shownin FIG. 4 having a vibration at a natural frequency four times that ofFIG. 3.

Now if the natural frequency of the blade corresponded to an integralnumber of running speed then the vibration shown in FIGS. 3 and 4 wouldbe order-related. Every time blade 78 passed sensor 77 and 76 therespective sensor would see the blade in exactly the same physicalposition (tangential deflection) with respect to the shaft position asshaft 20 rotates. If the vibration of blade 78 was not an integralnumber of times of the running speed then blade 78 would be in adifferent physical position each time it passed sensors 76 and 88respectively.

FIG. 5 shows blade 78 without vibration and blade 78''' withorder-related vibration phase shifted (at a different rpm or sensor) ascompared with blade 78' in FIG. 3.

FIG. 6 shows blade 78 without vibration and blade 78'''' withorder-related vibration phase shifted (at a different rpm or sensor) ascompared with blade 78''.

FIG. 7 shows one embodiment of the invention which may operate by usingonly one acoustic sensor 76. Acoustic sensor 76 is placed in location Aon housing 29 to receive acoustic signals 88 as shown in FIG. 7.Acoustic sensor 76 functions to receive acoustic energy in a frequencyrange from 0-25 kilohertz providing a corresponding acoustic signal. Theacoustic signal is coupled over lead 89 to an input of analog to digitalconverter 90 which converts the acoustic signal with an accuracy of 14bits after suitable low pass filtering to a frequency at no more thanhalf the sample rate to prevent aliasing. The output of analog todigital converter 90 is coupled over lead 91 to an input of memory 92.Memory 92 functions to store a record consisting of a plurality ofsamples obtained during each revolution of shaft 20 as a function of theshaft angular velocity (rpm) given at the beginning of a record whereina record consists of, for example, 64 samples per revolution as afunction of time.

Tachometer sensor 70 shown in FIGS. 1 and 7 is coupled over lines 71 and72 to an input of shaft speed detector 94 which provides an output overline 95 to an input cf address generator 96. Tachometer sensor 70functions to provide a reference signal over leads 71 and 72 indicativeof shaft 20 position and of rotor 30 position at least once each timeshaft 20 completes a revolution about the shaft axis 73 to provide anindication of angular velocity (rpm) of shaft 20. Shaft speed detector94 measures the time shaft 20 makes one complete revolution to determinethe angular velocity in revolutions per minute (rpm) for the nextrevolution. In a typical operating turbine operating at 3600 rpm the rpmmay vary plus or minus one rpm. The angular velocity of shaft 20 may besubdivided into sixteen increments between plus and minus one rpm toprovide each increment of 0.125 rpm. An accurate measure of the currentangular velocity of shaft 20 in rpm is essential so that data recordedper revolution which may comprise for example 64 to 128 samples isrecorded as a function of the rpm in memory 92. Address generator 96functions to generate an address as a function of the rpm of shaft 20which is coupled over lead 97 to memory 92 to store in memory 92 arecord of a plurality of samples for one revolution of shaft 20 before anew address generated as a function of the angular velocity of shaft 20is provided for the next record which may or not be the same angularvelocity as the prior revolution of shaft 20.

Address generator 96 also provides addresses over lead 97 for retrievinga record from memory 92 and coupling the record over lead 98 to an inputof synchronous averaging circuit 100. Synchronous averaging circuit 100also receives data from memory 102 over lead 104. Memory 102 may containfor example a running sum of the samples of records obtained atrespective rotor positions of the rotor along with the number of timesthe running sum has had samples added thereto. Synchronous averagingcircuit 100 may retrieve data from memory 102 on lead 104 and add thenext record samples respectively received over line 98 as well asprovide a count for the number of records added together which may bereturned to memory 102 for storage over lead 105. A running average canbe provided by also storing the average which may be obtained bydividing the running sum by the number of records added together at arespective rpm of shaft 20 and provide the average on lead 106 to aninput of sample alignment 120. Synchronous averaging circuit 100 andmemory 102 function to provide for averaging the amplitude and takinginto account the polarity of the samples obtained at respective rotorpositions within each revolution of shaft 20 revolving at a firstangular velocity and a similar but separate averaging of the amplitudeof the samples with shaft 20 revolving at a second angular velocity.Actually about 16 angular velocities in increments of 0.125 rpm arerecorded or accumulatively summed in memory 102.

Sample alignment 120 functions to curve fit the averaged samples at aparticular rpm and resample the curve to provide averaged samplescorresponding to common shaft positions at two shaft rpm's. Samplealignment 120 receives address signals generated as a function of therpm shaft 20 at the time the record was captured over lead 99. Theoutput of sample alignment 120 is coupled over lead 121 to an input ofmultiplexer 107.

Address generator 96 provides -addresses over lead 99 to memory 102 andaddress register 103. The addresses on lead 99 may correspond torespective rpm of shaft 20 and may be used for providing data tosynchronous averaging circuit 100 for averaging synchronously a numberof samples at respective rpm's or to provide two consecutive addressesrepresentative of two angular velocities of shaft 20 to memory 102 forproviding averaged data over lead 106 to sample alignment 120 which inturn provides the data by way of multiplexer 107 to subtractor 108. Datarepresentative of a first angular velocity is coupled over lead 109 toan input of subtractor 108. Data representative of a second angularvelocity is coupled over lead 110 to a second input of subtractor 108.Subtractor 108 functions to subtract the amplitudes and taking into theaccount the polarity of averaged samples obtained at respective rotor orshaft positions of shaft 20 revolving at the first and at the secondangular velocity to provide a difference Doppler signal at respectiverotor or shaft positions of the rotor whereby order- related backgroundnoise due to other blades having nonuniformity in angular position onthe rotor is removed. The difference Doppler signal is provided at theoutput of subtractor 108 on lead 112 to an output terminal and to theinput of comparator 114. A voltage potential representative of a voltagethreshold (V_(TH)) is coupled over lead 115 to a second input ofcomparator 114. Comparator 114 functions to compare the voltage V_(TH)with the potential on lead 112 containing the difference Doppler sampleto provide an output over lead 116 at times the difference Dopplersignal exceeds the threshold voltage indicating the presence of aresonantly vibrating blade or blade group within blade row 25 in highpressure turbine 16.

In operation of difference Doppler circuit 86 as shown in FIG. 7, shaft20 may have an angular velocity of 3600 rpm or 60 revolutions per secondwith analog to digital converter 90 taking a record of 64 samples perrevolution at 14 bits per sample which would result in a sampling rateof 3840 hertz. If data was accumulated for as long as 30 minutes, then108,000 records would be obtained. If the 108,000 records weredistributed over 16 angular velocity bins of 0.125 rpm each from 3599 to3601 rpm then on the average 6750 records would be in each angularvelocity bin. Address generator 96 would select two angular velocitiesbased on the largest number or records and the largest separation ofangular velocities prior to sending the averaged records at these twoangular velocities of shaft 20 to subtractor 108 to form the differenceDoppler signal. Since over a 6750 records will have been averaged, nonorder-related background noise and blade flutter (non order-relatedblade vibration) will be reduced by averaging wherein the order-relatedbackground noise and blade vibration will accumulate and be enhanced.When the two averaged order-related records are subtracted from oneanother, taken at different angular velocities of shaft 20,order-related signals due to blade row nonuniformity will be cancelledout whereas order-related resonantly vibrating blades will remain due toa difference in resonant blade phase at common rotor positions. Thephase difference in blade vibration is a function of the difference inrpm of shaft 20.

The signals or records retrieved from memory 102 on line 106 aresynchronous averaged records which may be for example averaged over 2000to 10,000 records within a respective angular velocity bin of shaft 20in memory 102.

Address register 103 may hold the address used to access memory 102 andsample alignment 120. The address may be an indication of the rpm ofshaft 20 corresponding to the record retrieved from memory 102 on lead106 or on lead 121. The output of address register 103 may provide notonly the rpm of the two records subtracted but also of the sample numberin the record indicative of the location on the blade row or the bladeat times comparator 114 provides an output on line 116. The output ofaddress register 103 as shown in FIG. 7 is on lead 118.

If the sampling rate is independent of the rpm of shaft 20, then priorto subtracting the records obtained at two rpm's or angular velocitiesof shaft 20, one of the records will need to be shifted in order thatthe samples subtracted will correspond to the same physical location ofthe moving blade row 25 passed sensor 76. The records may be lined up bycurve fitting the 64 samples to a 25 order curve fit formula followed byresampling the curve corresponding to obtaining two averaged samples atrespective angular position of shaft 20. Sample alignment 120 performsthis function and provides an output over lead 121 to multiplexer 107.

FIG. 8 shows a first alternate embodiment of the invention wherein thelocation of the resonantly vibrating blade may be located and thefrequency of its vibration determine from the difference Doppler signalon lead 112 from difference Doppler circuit 86 shown in FIGS. 7 and 8.Referring to FIG. 8, lead 118 is coupled to a first input of HilbertTransform 124 which contains the address indicative of rpm and dataposition with respect to shaft 20 of the data transferred over on lead112 which is coupled to a second input of Hilbert Transform 124. Byusing the Hilbert Transform, the normal real valued time domainfunctions are made complex, which yield two useful properties, theenvelope and the instantaneous frequency. The maximum amplitudedetermines the location of the vibrating blade since the amplitude ofthe vibrating blade will be maximum as it passes sensor 76. Theinstantaneous frequency at the time the vibrating blade passes 76 willbe the resonant frequency of the vibrating blade since it will be movinglaterally with respect to acoustic sensor 76. The Hilbert Transform ismanifested by the fact that all the normal real-valued time domainfunction (correlation impulse response etc.) are in fact complex-valuedfunctions because the imaginary part of a function is the HilbertTransform of the real part. The time domain functions can be displayedsimilarly to the frequency domain functions in terms of their real part,imaginary part, magnitude, and phase versus time. The magnitudedescribes the envelope of a signal. The phase representation allows thedetection of instantaneous frequency, which is of importance for signalssweeping in frequency with time i.e. a Doppler signal. While the FourierTransform moves the independent variable of a signal from the time tothe frequency domain or vice versa, the Hilbert Transform leaves thesignal in the same domain. The Hilbert Transform of a time signal isanother time signal and the Hilbert Transform of a frequency "signal" isanother frequency signal. A nonmathematical way of describing theHilbert Transform of a time signal is to say that it gives all thefrequency components of a signal a minus 90 degree phase shift or in thetime domain that it shifts each component by 1/4 wavelength. This effectis similar to the integration of the signal. As an example, the HilbertTransform of a sinusoid, for example, cos 2 π ft is sin 2 π ft. TheHilbert Transform of sin 2 π ft is -cos 2 π ft. With but depends on thewavelength of frequency of the particular component. The HilbertTransform of a real-valued time signal, a(t), is defined as: ##EQU1##

The Hilbert Transform is further described in a paper entitled "TheHilbert Transform" by N. Thrane, Technical Review, No. 3, 1984 publishedby A. Bruel & Kjaer publications, ISSN 007-2621.

The steps in signal processing performed by Hilbert Transform 124 willnow be described to provide the amplitude peak over lead 125 with theblade position or blade number provided over lead 127. Furtherprocessing will yield the instantaneous frequency at the blade positionof an amplitude peak to provide the frequency of the resonating bladeover lead 128.

The first step taken in Hilbert Transform 124 is to record the amplitudeand taking into account the polarity of the difference Doppler signal onlead 112 as a function of time or angular position of rotating shaft 20on lead 118.

The second step is to transform the time domain signal to the frequencydomain as a function of the order of running speed or angular velocityof rotating shaft 20.

The third step is to obtain the Hilbert Transform by shifting back 90degrees in phase every frequency component of the frequency domain curveformed in step 2 with the base line being the same as in step 2 i.e. afunction of the order of running speed.

The fourth step is to take the inverse Fourier transform of the data orof the curve formed in step 3 to provide data or a curve in the timedomain as a function of one revolution of shaft 20 which is the samebase line as used in step 1.

The fifth step is to take the Hilbert magnitude of the Hilbert Transformin step 4 using the same base line as in step 4 i.e. a function of onerevolution of shaft 20. The amplitude peak in the data or curve formedin step 5 is an indication of the position of a resonantly vibratingblade.

In step 5, the Hilbert magnitude is determined by taking the square rootof the sum of the amplitudes squared at each base line point of theoriginal signal in step 1 plus the sum of the amplitudes in step 4squared corresponding to the same base line points.

In step 6 the function cos 2 π ft. between plus one and minus 1 isplotted versus the same base line as used in step 5 and using the datafrom step 1 divided by the data from step 5. In other words, in step 6,the data point (ordinate) of step 1 as a function of the base lineposition (abscissa) is divided by the data point (ordinate)corresponding to the same base line position obtained in step 5.

In step 7, the instantaneous phase cos⁻¹ φ (t) is determined or plottedby determining the inverse of the cosine function determined in step 6.The same base line or abscissa is used in step 7 as used in steps 1, 4,5 and 6.

In step 8, the instantaneous phase is φ(t) from step 7 is differentiatedwith respect to time (dt) and plotted as a function of the base line asused in FIG. 7, i.e. one revolution of shaft 20. The position on thebase line or abscissa of the peak amplitude obtained in step 5corresponds to the position to find the instantaneous frequency in step8 and is the frequency of the resonantly vibrating blade causing theamplitude peak in step 5, for example, a blade in blade row 25 of highpressure turbine 16 shown in FIGS. 1 and 2.

Referring to FIG. 9, a second alternate embodiment of the invention isshown for detecting a resonantly vibrating blade attached to shaft 20 ofa rotating rotor in an operating turbine row 25. As shown in FIGS. 1 and2 a second acoustic sensor 77 is shown having a portion at location 130inside housing 29. Acoustic sensor 77 receives acoustic signals 131 fromlocation B at 130 as shown in FIG. 9. Difference Doppler circuit 86corresponds to the embodiment shown in FIG. 7 and receives acousticsignals 88 from location A at 87. Difference Doppler circuit 136corresponds to difference Doppler circuit 86 except it is coupled toacoustic sensor 77 in place of acoustic sensor 76. Acoustic sensor 76 isspaced apart from acoustic sensor 77 by a separation angle correspondingto an angle of rotation of shaft 20 to receive sound waves emanatingfrom the vibrating blade of blade row 25 shown in FIG. 1 as the bladerotates about its rotor axis 73 to provide an acoustic signal from eachacoustic sensor from the received sound waves.

Each acoustic sensor 76 and 77 are positioned with respect to rotor 30and blade row 25, preferably downstream, so that the blade approachesand departs from each acoustic sensor in the course of one rotation ofshaft 20 and of rotor 30 about the rotor axis 73 thereby imparting aDoppler effect to the received sound waves.

Phase shift circuit 140 as shown in FIG. 9 functions to provide samplealignment so that the samples correspond to the same position along therotor for removing order-related background noise due to blade rownonuniformity etc. Phase shift circuit 140 receives over lead 138 thedifference Doppler signal from difference Doppler circuit 136 as well asan address over lead 138 and a difference Doppler signal over lead 112from difference Doppler circuit 86 as well as an address over lead 118.Phase shift circuit 140, which may be for example a computer, functionsto phase shift or transform the difference Doppler samples at one or ateach sensor in time to correspond to the same location on rotor 30 orblade row 25 at the time the samples were taken to provide transformeddifference Doppler samples with respect to each sensor 76 and 77. Asdescribed with respect to sample alignment 120 the record consisting ofsamples of 1 revolution of the difference Doppler signal may be curvefitted with a formula or curve fitting equation to the 25th order andresampled to provide the appropriate phase shift to match the blade rowlocations respectively where the other difference Doppler signal sampleswere captured; or both signals on lines 112 and 138 may be curved fittedand resampled. The output of phase shift circuit 140 is coupled overlead 142 to an input of amplitude normalization circuit 144. Amplitudenormalization circuit 144 functions to adjust the amplitude of onedifference Doppler signal for example the signal on lead 118 so that iscompensates for variation in sensor and circuit gain with the differenceDoppler signal on lead 132. Difference Doppler signal on lead 132 isalso coupled to amplitude normalization circuit 144 as a referencesignal.

The output of amplitude normalization circuit 144 which is the samesignal as on lead 142 but adjusted in amplitude is coupled over lead 146to an input of subtractor 148. Subtractor 148 which may for example acircuit or a computer functions to subtract the difference Dopplersignal on lead 146 from the difference Doppler signal on lead 132 toprovide a difference-difference Doppler signal on lead 150. A signalindicative of the address or blade position is provided on lead 138 withrespect to the output of subtractor 148 on lead 150. The output ofsubtractor 148 is coupled over lead 150 to an input of comparator 152.Comparator 152 has a second input over lead 154 which is coupled to avoltage V₁ for thresholding the signal on lead 150 to provide an outputon lead 156 at times the signal on lead 150 exceeds the potential oflead 154. An output from comparator 152 on lead 156 is an indicationthat there is a resonantly vibrating blade which may be, for example, inblade row 25 of high pressure turbine 16. The location of the vibratingblade may be provided by the address signal or blade position signal onlead 138.

Referring to FIG. 10, an improved method and apparatus is shown forlocating the resonantly vibrating blade or blade group and fordetermining the frequency of the resonantly vibrating blade. Leads 138and 150 of difference-difference Doppler circuit 129 are coupled torespective inputs of Hilbert Transform 124. Hilbert Transform 124performs the same steps as previously described with respect to FIG. 8to determine the amplitude maximum on lead 125, the blade number on lead127 and the instantaneous frequency on lead 128. The instantaneousfrequency at the amplitude peak corresponds to the frequency of theresonantly vibrating blade or blade group.

Referring to FIG. 11 a fourth alternate embodiment of the invention isdescribed for detecting and locating fluttering blades which are selfexcited nonresonantly vibrating blades vibrating at a natural frequencyof the blade or a harmonic thereof. Blade vibrations can be classifiedin one of two general categories, order-related or non order-related.Order-related vibrations occur at exact integer multiples of runningspeed. For example, a blade with a natural frequency very close to 4 perrevolution vibrates resonantly at exactly four (4) per revolution. Onthe other hand, a blade may vibrate or flutter in self excited fashionright at the natural frequency, but not exactly at four per revolutionand thus not order-related. An order-related vibration, or anorder-related signal repeats exactly in each revolution; while a nonorder-related vibration or signal does not. An order-related bladevibration results in an order-related Doppler signal in a downstreamacoustic sensor. A nonperfect geometric blade row (blade to blade)results in an order-related non Doppler signal in a downstreammicrophone. A non order-related blade vibration results in a nonorder-related signal in a downstream microphone or sensor, but with anorder-related amplitude envelope that peaks up as the vibrating bladepasses by the sensor. Non order-related background steam noise in a highpressure steam turbine results in a non order-related signal in thedownstream acoustic sensor 75 shown in FIG. 11, but with "straight line"amplitude envelope.

The apparatus of FIG. 8 as shown, cannot be used for detecting afluttering or non order-related vibrating blade, since synchronousaveraging circuit 100 functions by synchronous averaging the acousticsignal to remove the non order-related content of the acoustic signal online 98 shown in FIG. 8. This occurs even though the amplitude envelopeof non order-related content of the signal on line 98 is order-related,the signal itself is not, and thus the non order-related signal wouldaverage away.

Signal processor 160 shown in FIG. 11 provides a means for detecting theorder-related envelope associated with a blade vibrating in a nonorder-related manner such as in fluttering and to do so in the presenceof non order-related "straight line" background noise, and in thepresence of order-related noise either from blade row nonuniformity, andfrom other order-related sources including blade resonance. In FIG. 11,like references are used for functions corresponding to the apparatus ofFIG. 7. The signal on line 98 represents the acoustic signal fromacoustic sensor 76 positioned downstream on a stationary member withrespect to shaft rotor 30 shown in FIG. 1 to receive soundwaves oracoustic signals 88 emanating from the vibrating blade or rotor 30 asthe blade rotates about the rotor axis 73. The acoustic signal fromacoustic sensor 76 is digitized and sampled by analog to digitalconverter 90 and by address generator 96' which stores the digitizedsignal on line 91 in memory 92. The sampling may be at a rate such as 64or 128 samples per revolution. The sampling may be proportional torunning speed putting the samples in the revolution domain. Alternately,the samples may be evenly spaced apart from a start mark originatingfrom the tach sensor 70. Each record consisting of 64 or 128 samplesrepresent one revolution starting at the tach trigger from tach sensor70 which is tagged with a label indicating the exact angular velocity ofshaft 20 and rotor 30 at the time of capture of the record. Asdescribed, with respect to FIG. 7 there may be 100 speeds spanning plusor minus 1 rpm for a rotor having an angular velocity of 3600 rpm. If 64samples were taken per record, then 1024 individual point-speed binswould be stored in memory 102. Synchronous averaging circuit 100 andmemory 102 function to provide a running synchronous average over aperiod of time for example a half hour or an hour before being droppedout. The output of memory 106 is coupled over lead 162 to an input ofsubtractor circuit 164. The output of memory 92 on lead 98 is coupled toa second input of subtractor circuit 164. For each new record obtainedfrom memory 92 corresponding to one of the sixteen speeds or angularvelocities as determined by address generator 96', the corresponding 64points of the running synchronous average from memory 102 at therespective angular velocity is first algebraicly subtracted from the newrecord in subtractor circuit 164. The output of subtractor circuit 164is coupled over lead 165 to an input of memory 166 which stores inmemory 166 a different signal sample at 1024 points speed bins. Addressgenerator 96' couples an appropriate address over lead 167 to memory 166so that different signal samples on lead 165 are stored as a function ofrotor position and angular velocity. Subtractor circuit 164 functions tosubtract the amplitude of averaged samples obtained at respective rotorpositions of rotor 30 revolving at each angular velocity of theplurality of angular velocities or 100 speeds from individual samplesobtained at respective rotor positions of rotor 30 revolving at eachangular velocity of the plurality of angular velocities to provide adifference signal sample at respective rotor positions of rotor 30revolving at the plurality of angular velocities. Memory 166 containsnon order-related background noise due to flow noise and nonorder-related vibrating blades.

Address generator 96' functions to generate addresses over leads 167 andlead 169 to provide addresses to memories 166 and 170 respectively whichcorresponding to the same rotor position and rotor angular velocity. Theoutput of memory 166 is coupled over lead 171 to an input of root meansquare difference circuit 172. Root mean square difference circuit 172functions to take the square root of the sum of the squares of thedifference signal sample from memory 166 and the difference signalsamples obtained earlier at the same respective rotor position and atthe same angular velocity which had been stored in memory 170. Memory170 supplies a signal over lead 173 which may be for example a runningsum of the squares of previous difference signal samples stored inmemory 170 with respect to a rotor position and angular velocity. Theoutput of root mean difference circuit 172 is coupled over lead 174 tomemory 170. Memory 170 has 1024 root mean square difference samplesstored therein corresponding to respective rotor positions and rotorangular velocity.

Address generator 96' provides addresses over line 169 to read out theroot mean square difference samples at respective rotor positions and atone angular velocity which is coupled over lead 175 to an input of rootmean square running speed circuit 176 and to an input of subtractorcircuit 180. Root mean square running speed circuit 176 functions todetermine the root mean square of the root means square differencesamples at respective rotor positions of rotor 30 revolving at eachangular velocity of the plurality of velocities to form a root meansquare running speed signal with respect to each angular velocity. Theoutput of root mean square running speed circuit 176 is coupled overlead 182 to a second input of subtractor circuit 180.

Subtractor circuit 180 functions to subtract the amplitude of the rootmean square running speed signal on lead 182 at each respective angularvelocity of rotor 30 from the amplitude of the root mean squaredifference samples on lead 175 at the same corresponding angularvelocity of rotor 30 to form reduced mean square difference samples atrespective rotor positions and angular velocities which are coupled overlead 184 to an input of memory 186 which stores the samples. Addressgenerator 96' provides addresses over lead 187 to memory 186 to locatethe samples received on lead 184. Memory 186 thus holds 1024 reducedroot mean square difference samples corresponding to 64 rotor positionsand 16 angular velocities. The output of memory 186 when providedaddresses by address generator 96' over lead 187 is coupled over lead188 to an input of synchronous averaging circuit 190. Synchronousaveraging circuit 190 functions to average over several revolutions forexample 128 revolutions of rotor 30 the reduced means square differencesamples at respective rotor positions of the rotor revolving atrespective angular velocities. Memory 192 functions to hold the averagesof the reduced means square difference samples by summing the samples asa running sum and dividing by the number of records stored. Addressgenerator 96' provides appropriate addresses over lead 194 to an addressinput of memory 192 and to an output indicative of rotor position.Synchronous averaging circuit provides data to memory 192 over lead 195and receives data from memory 192 over lead 196.

A non zero result from synchronous averaging circuit 190 after manyaverages for example 128 averages indicates an order-related envelope ofa non order-related signal i.e. a fluttering blade. Memory 192 maycontain 1024 averaged and reduced root mean square difference samplescorresponding to 64 rotor positions and 16 angular velocities. Addressgenerator 96' provides addresses over lead 194 to memory 192 to provideover lead 198 each averaged and reduced root mean square differencesample to comparator 200. A second input to comparator 200 is athreshold voltage V_(TH) over lead 202. Comparator 200 functions tocompare the averaged and reduced root mean square difference samplescorresponding to respective rotor positions of said rotor revolving atrespective angular velocities with the threshold value V_(TH) wherebyamplitudes above the threshold value V_(TH) are indicative of a nonorder-related vibrating blade. The position of the vibrating blade isindicated by the address on lead 194 at the time the comparator 200provides an output on lead 204.

Referring to FIG. 12 a signal processor 210 is shown for detecting anaerodynamic event in an operating turbine for example low pressureturbine 18 shown in FIG. 1. In FIG. 12, like references are used forfunctions corresponding to the apparatus of FIG. 11. An aerodynamicevent in an operating turbine is typically non order-related, that is,independent of rotor position. One example of an aerodynamic event iscondensation shock in an operating steam turbine where pressure andtemperature conditions with respect to or in between turbine blade rowspermit the steam to condense. The condensation is a very localized eventin a particular blade row or in between blade rows and may move upstreamor downstream. In FIG. 12 the difference signal sample at respectiverotor positions of the rotor revolving at a plurality of angularfrequencies on lead 71 is coupled to an input of comparator 212. Athreshold voltage V_(TH) is coupled over lead 214 to a second input ofcomparator 212. Comparator 212 functions to provide an output over lead216 at times the difference signal sample exceeds the threshold voltageV_(TH). Lead 216 is coupled to an external terminal indicative of anaerodynamic event and is coupled to an input of counter 218 which incooperation with memory 220 counts the number of consecutive cycles orrevolutions of rotor 30 where difference signal sample on lead 171excess the voltage threshold on lead 214. The output of counter 218 iscoupled over lead 221 to an input of memory 220. The output of memory220 is coupled over lead 222 to an input of counter 218. Addressgenerator 96'' provides appropriate addresses over lead 224 indicativeof rotor position and angular velocity of rotor 30. An output on lead216 is indicative of an aerodynamic event due to a non order-relatedsignal received by acoustic sensor 76 which may be due for example fromcondensation shock or rotating stall. Rotating stall is a phenomenon ina turbine where for some reason the flow of steam or gas isaerodynamically stalled on one or several blades in a blade row which inturn causes the gas to stall on other turbine blades adjacent to theprevious stalled turbine blades. In a rotating stall several turbineblades are stalled in a blade row and the affected blades move aroundthe blade row as described by the term rotating stall. An output on lead222 provides the number of consecutive cycles that an aerodynamic eventhas occurred. Where several cycles are indicated on lead 22 anaerodynamic event is confirmed with high confidence. The output on lead224 provides an indication of the rotor position and angular velocity ofrotor 30 at time of the aerodynamic event. By comparing the rotorposition on a revolution by revolution basis, a condensation shock whichdoesn't move with respect to rotor position may be distinguished with arotating stall which does move with respect to rotor position.

In FIG. 12, synchronous averaging circuit 100, memory 102 and subtractorcircuit 164 and memory 166 function to remove the order-relatedcomponents from the samples on line 98. The aerodynamic event is by farthe largest pressure amplitude source which is non order-related.Typically, several consecutive revolutions of rotor 30 with theamplitude on lead 171 exceeding a predetermined threshold would berequired to signal the existence of an aerodynamic event on lead 222.Alternately, an aerodynamic event may be indicated or the beginning ofan aerodynamic event may be indicated by an output on lead 216 whichindicates each time or each revolution in each rotor position where thesignal on lead 171 exceeds the voltage threshold.

Referring to FIG. 13, signal processor 226 is shown for detecting anaerodynamic event in an operating turbine and for determining theaerodynamic event is a condensation shock or a rotating stall. In FIG.13, like references are used for functions corresponding to theapparatus of FIG. 12. Signal processor 210 which is shown in more detailin FIG. 12, has lead 216 coupled to an input of time difference circuit228. Signal processor 210' which is the same as signal processor 210except for the location acoustic sensor 76 which may be substituted withacoustic sensor 77 positioned at location B or location 130 shown inFIGS. 2 and 9. With two acoustic sensors 76 and 77 at locations 87 and130 respectively, shown in FIG. 2, they are positioned at the samelongitudinal or axial position on rotor 30 but separated by an angle ofrotation of rotor 30. No time delay between outputs on leads 216 and216' shown in FIG. 13 may indicate condensation shock on lead 230. Lead216' is coupled from signal processor 210' to a second input of timedifference circuit 228. Time difference circuit 228 functions todetermine on a revolution by revolution basis the time differencebetween signals on leads 216 and 216'. If there is no time differencebetween signals on leads 216 and 216', then time difference circuit 228provides an output on lead 230 indicative of condensation shock. If timedifference circuit 228 records a fixed time delay between signals onleads 216 and 216' on a revolution by revolution basis, then an outputis provided on lead 231 indicative of rotating stall. It is understoodthat the signals on leads 216 and 216' are non order-related signals.Time difference circuit 228 may also be coupled to leads 224, 220 20 ofsignal processor 210 and leads 224' and 220' of signal processor 210' toperform additional computations to confirm that condensation shock or arotating stall has occurred. The major difference between the twoaerodynamic events being the time lag of the non order-related signaldetected at sensors 76 and 77 at locations 87 and 130 respectively.

Referring to FIG. 14, a monitor 236 is shown for detecting differentialnozzle wear for example nozzle sections 237 and 238 shown in FIG. 1 ofhigh pressure turbine 16. As shown in FIG. 1, four nozzle sections237-240 may be positioned every 90 degrees upstream of blade row 25.Nozzle section 237 is on the top while nozzle section 239 is on thebottom and not shown. Downstream of blade row 25 and downstream ofnozzles sections 237 and 239 may be positioned at location A andlocation C acoustic sensors 76 and 242 respectively. Location Ccorresponds to location 241 shown in FIG. 2 which is inside the housing29 or turbine 16. Acoustic sensor 242 is also shown in FIG. 2. Theoutput of acoustic sensor 242 is coupled over lead 243 to an input ofsignal processor 244. In FIG. 14, like references are used for functionscorresponding the apparatus of FIG. 7. Signal processor 244 performs thesame functions as analog to digital converter 90, memory 92, synchronousaveraging circuit 100, and memory 102 interconnected as shown in FIG. 7.Signal processor 244 functions to obtain samples from acoustic sensor 76and to synchronously average the samples as a function of angularvelocity of rotor 30 shown in FIG. 1 which are stored in memory 102. Theoutput of signal processor 244 is coupled over lead 245 to an input ofphase shift circuit 246. Phase shift circuit 246 functions to shift thesecond samples of the second acoustic signal to correspond to the sameplace on rotor 30 as samples of the first acoustic signal. The output ofphase shift circuit 246 is coupled over lead 247 to an input ofsubtractor circuit 248. It is noted that lead 243 corresponds to lead 89and lead 245 corresponds to lead 106 in FIG. 7. Lead 106 is coupled to asecond input of subtractor circuit 248. Samples are fed to subtractorcircuit 248 in response to addresses generated by address generator 96so that samples of the first and second acoustic signal are subtractedtogether corresponding to the same place on the rotor 30 of turbine 16.The signals on lead 106 and 247 are for the most part order-relatedsignals inasmuch as non order-related signals have been minimized bysynchronous averaging circuit 100. With respect to the first acousticsignal and the synchronous averaging circuit 100 will then signalprocess 244 with respect to the second acoustic signal. Thus, subtractorcircuit 248 is subtracting two order-related signals corresponding tothe same position on rotor 30 to provide a difference signal on lead250. The magnitude or amplitude of the signal on lead 250 is anindication of nozzle wear for the nozzle section upstream of acousticsensors 76 and 242 respectively.

In FIG. 14, said each acoustic sensor 76 and 242 sees an order-relatedsignal from the same place on the blade row 25 of rotor 30, separated inphase or time, the only major difference in the two acoustic signalsafter being corrected for this phase or time difference, must be due toa difference in the level of gas or steam flow. A difference in theamount of nozzle wear between nozzle sections 237 and 239 upstream ofsensors 76 and 242 respectively, results in a difference in steam flowwhich results in a difference in the amplitude of the order-relatedsignal picked up via the acoustic signals 88 and 251 at acoustic sensors76 and 242. Acoustic sensors 76 and 242 should be able to withstand ahigh pressure of greater than 3000 pounds per square inch whichcorresponds to 465 pounds per square centimeter. Sensors 76 and 242should also withstand a high temperature of greater than 1000° F. whichcorresponds to 537.8° C.

Referring to FIG. 15, a monitor 254 is shown for measurement oforder-related torsional resonant shaft vibrations in an operatingturbine. In FIG. 15, like references are used for functionscorresponding to the apparatus of FIGS. 7 and 8. In FIG. 15, lead 118 iscoupled to an input of sine wave detector 256. Lead 112 is also coupledto an input of sine wave detector 256. Lead 125 from Hilbert Transform124 is coupled to an input of sine wave detector 256. Lead 127 from anoutput of Hilbert Transform 124 is coupled to an input of sine wavedetector 256. Monitor 254 recognizes the fact that torsional shaftvibration, for example shaft 20 shown in FIG. 1, projects out into largetangential blade vibration at the blade tips of large turbines. Iftangential blade vibration is order-related, it repeats in eachrevolution. If the tangential blade vibration is resonant, thetangential blade vibration will vary its phase as a function of speed.If tangential blade vibration is highly resonant, i.e. a very closematch between the effected order of running speed and the naturalfrequency of the tangential blade vibration, and if the sampling is low,then the resulting tangential blade tip vibrations can be uncoveredusing the embodiment shown in FIG. 15. Unlike the single resonant bladein a blade row where the Hilbert magnitude looks like one peak withinthe revolution of shaft 20, the Hilbert Magnitude looks like a sine wavewith the number of cycles within a revolution of shaft 20 correspondingto the number of orders of the torsional vibration. In operation ofmonitor 254, the Hilbert amplitude including the amplitude maximum iscoupled out on lead 125' to sine wave detector 256. Sine wave detector256 functions to analyze the amplitude on lead 125' with respect to eachrevolution to detect an amplitude sin wave of one or more cycles perrevolution. Lead 127 provides the blade number or location of amplitudepeaks per revolution. Alternately, sine wave detector may look at theraw data supplied over lead 118 and 112 to determine whether theamplitude is varying according to a sine wave function per revolution.Sine wave detector 256 may provide an output on lead 257 indicative oftorsional vibration of shaft 20. Sine wave detector 256 may provide anoutput on lead 258 indicative of the frequency of the torsional shaftvibration.

Referring to FIG. 16, monitor 260 is shown for measuring theorder-related torsional resonant shaft vibration in a turbine. In FIG.16, like references are used for functions corresponding to theapparatus of FIG. 15. In FIG. 16, difference-difference Doppler circuit129 is substituted for difference Doppler circuit 86. Sine wave detector256 functions the same in FIG. 16 as it did in FIG. 15.

Referring to FIG. 17, a typical Campbell diagram for a low pressureturbine blade is shown. In FIG. 17, the ordinate represents frequency inhertz and the abscissa represents turbine speed N in revolutions perminute (rpm). In FIG. 17, the space between curves 268 and 269 representa narrow zone where the first natural frequency of a turbine bladeoccurs. The space between curves 270 and 271 represent a narrow band offrequencies where the low pressure blade vibrates at twice its naturalfrequency. The space between curves 272 and 273 represent the narrowband of frequencies where the low pressure turbine blade vibrates atthree times its natural frequency. In FIG. 17, curves 276-281 plot thefirst through sixth harmonic respectively of turbine speed. Frequencyand cycles per second equals the order of harmonic times N (turbinespeed) (rpm)/60. As shown in FIG. 17, high amplitude resonant vibrationscan occur where an forcing frequency i.e. running speed closely matchesa natural vibration frequency of a turbine blade. However, for theturbine blade vibration to be really severe, the forcing frequency andnatural frequency must be extremely close, the damping for the effectivemode must be very low, and the forcing mechanism must be such as to beable to drive the mode effectively.

Where the forcing and natural frequencies do not exactly match, it isimportant to realize that the vibration takes place at the forcingfrequency, not at the natural frequency of the blade. Forcingfrequencies exist at all the integer multiples of running speed, butsome of these are obviously more significant than others.

One prevalent forcing component for turbine blades is at nozzle passingfrequency. This arises from the impulse a blade receives as it passeseach nozzle wake. Since these impulses are not perfectly sinusoidal inform, harmonics of nozzle passing frequency also will be present.

In addition, any repetitious flow nonuniformities within the rotationalcycle such as those arising from the horizontal split of the nozzleblocks and casing, from internal struts, inlet or exhaust openings, orany variation nozzle to nozzle, all cause forcing frequencies atonce-per-rev and its harmonics. Even when nozzle spacings, strutspacings, or other spacings are not integer submultiples of arevolution, just as long as a pattern, no matter how unusual, repeats inevery revolution, the excitation frequencies will be exact integermultiples of rotational speed.

The amplification factor associated with a resonant vibration dependsupon both the degree of frequency math between the driving frequency andthe natural frequency and on the damping associated with that mode. Thedamping is often given in terms of the amplification factor for aperfect match. Here factors of several hundred are not uncommon forblade modes. But a mode with an amplification factor of 400 for aperfect frequency match drops to an amplification of less than 50 forjust a one percent mismatch. Therefore, a near perfect frequency matchis required for severe high amplitude resonants of the turbine blade.

Thus, with typical manufacturing variations, only a few of the blades orblade groups in a given row might be vibrating excessively at any onetime, even in a problem situation.

Finally, whether a particular mode can be efficiently driven depends onhow the driving forces line up spacially and temporally with the modeshape. In short, are the forces on one part of the structure workingwith or against the forces on the other parts of the structure? In thecase of the first bending mode of a blade corresponding to the firstnatural frequency of the blade, the whole blade moves in the samedirection at the same time, and thus all the dynamic forces acting alongthe blade work together. However, for the second bending mode, or secondnatural frequency, the upper part of the blade moves one way while thelower part moves another. Thus, if the forces on the upper part of theblade are supporting the motion, the forces on the lower part areopposing it. Then, the result is that a reduced effective force acts toexcite the mode. This description, though somewhat simplistic, explainswhy the higher order modes are less likely to be strongly excited. Forblade group modes forces can work against each other at the differentcircumferential locations as well.

Turbine manufactures, in designing low pressure blades and blade groups,attempt to avoid the possibility of forced resonant vibration. Asillustrated in FIG. 17 by the Campbell diagram, the goal of the turbineblade designer is to avoid intersecting the harmonic lines, curves276-281, with the first few lateral and torsional frequencies, when atoperating speed i.e. the natural frequencies between curves 268-269,270-271, and 272-273. In practice, this requires a sufficient marginbetween the forcing and natural frequencies so that statisticalvariations in blade attachments, material nonuniformities andmanufacturing tolerances can be accommodated. As shown in FIG. 17, thenatural frequencies of blade vibration changed slightly with rotationspeed of shaft 20 or of rotor 30 as shown in FIG. 1. The change innatural frequency of the vibrating blade is due to centrifugal loadingeffects, and must be determined by testing.

Despite careful design and testing, it is not practical to dynamicallyevaluate each blade under operating conditions. With the uncertaintiesin individual blade parameters and the fact that the higher modes areusually neglected, one or more turbine blades in a given low pressureturbine stage may be resonant at or close to one of the forcingfrequencies. Such a blade may have a sufficiently high amplitude ofvibration and steady stress level to cause fatigue cracking, especiallyif corrosion is also present.

The turbine speed may be for example 3600 rpm which is shown in FIG. 17by line 282.

FIG. 18 shows an exciter 284 for inducing torsional vibrations intoshaft 20 of a running turbine 14 for the purpose of determining aCampbell diagram under normal operating conditions. Exciter 284 may becoupled directly to shaft 20 as shown in FIG. 18 which may be a motor toinduce torsional vibrations on shaft 20. Alternately, exciter 286 may becoupled to the rotating magnetic field of electric generator 64 toprovide amplitude modulation to the magnetic field at frequencies at ornear tangential vibration modes i.e. natural frequencies of the turbineblades. The power required for excitation by exciter 286 is limited tothe maximum voltage variation allowable for on line conditions ofelectric generator. The power required from exciter 286 is relativelylow if the excitation input is at the direct current field windings ofelectric generator 64. The power required from exciter 286 is limited bythe inductance of electric generator 64 and limited by the hysteresislosses inherent in generator 64. The induced torsional vibrations may befor example in the range from 140 to 150 hertz. Torsional oscillation orvibration of shaft 20 should be sufficient to deflect the turbine bladeat its end by about 0.00254 centimeters (0.001 inches).

In FIG. 18, exciter 286 may be coupled to alternator or electricgenerator 64 over leads 287 and 288. Leads 288 and 287 may be coupled tothe field windings of electric generator 264. The power supplied overleads 287 and 288 to provide adequate torsional vibration has been foundto be a few percent of the power generated by the electric generator 64.Exciter 286 may have a frequency control circuit within it to vary thefrequency from 0-200 hertz for example. It is noted that in FIG. 17 thefirst natural frequency between curves 268 and 269 normally occur in thevicinity of 150 hertz.

Individual axial vibration may be induced by a fixed coil mounted withina nozzle block blade or by a series of coils spaced around the block toprovide excitation at the range of frequencies of interest.

In operation, the Campbell diagram may be determined by varying thetorsional vibration over a range of predetermined frequencies and at thesame time monitoring non order-related blade vibration using the signalprocessor shown in FIG. 11.

What is claimed is:
 1. An apparatus for detecting a vibrating blade of arotating rotor in an operating turbine comprising:an acoustic sensorpositioned on a stationary member with respect to said rotor to receivesound waves emanating from said vibrating blade of said rotor as saidblade rotates about said rotor axis and to provide an acoustic signalfrom said received sound waves, said acoustic sensor positioned withrespect to said rotor so that said blade approaches and departs fromsaid acoustic sensor in the course of one rotation of said rotor aboutsaid rotor axis thereby imparting a Doppler effect to said receivedsound waves, first means for obtaining a reference signal indicative ofrotor position at least once each time said rotor completes a revolutionabout said rotor axis and for determining the angular velocity of saidrotor, second means for sampling said acoustic signal to obtain samplesas a function of rotor position as said rotor completes a plurality ofrevolutions at a first and at a second angular velocity of said rotor,third means for averaging said samples obtained at respective rotorpositions of said rotor revolving at said first angular velocity andrevolving at said second angular velocity, fourth means for subtractingthe averaged samples obtained at respective rotor positions of saidrotor revolving at said first and at said second angular velocity toprovide a difference signal at respective rotor positions of said rotorwhereby order-related background noise due to other blades havingnonuniformity in angular position on the rotor is removed, and fifthmeans for comparing the amplitude of said difference signal atrespective rotor positions of said rotor with a threshold value wherebyamplitudes above said threshold value are indicative of said vibratingblade.
 2. The apparatus of claim 1, wherein said first means includessixth means for obtaining a reference signal from the shaft of therotor.
 3. The apparatus of claim 1, wherein said second means forsampling includes sixth means for sampling at said first and secondangular velocity where said first and second angular velocity are spacedapart by at least one revolution per minute.
 4. The apparatus of claim1, wherein said third means for averaging includes sixth means foraveraging sampled over at least one thousand revolutions of said rotor.5. The apparatus of claim 1, wherein said fifth means includes sixthmeans for determining the rotor position at the peak amplitude of saiddifference signal at times the difference signal exceeds the thresholdvalue.
 6. The apparatus of claim 5, wherein said sixth means includesseventh means for determining the frequency of said difference signal atsaid peak amplitude.
 7. The apparatus of claim 6, wherein said seventhmeans includes eighth means for determining the instantaneous phase ofsaid difference signal at said peak amplitude.
 8. The apparatus of claim7, wherein said seventh means include ninth means for differentiatingthe instantaneous phase of said difference signal.
 9. The apparatus ofclaim 5, wherein said sixth means includes seventh means for obtainingthe difference signal in the frequency domain and eighth means forobtaining the Hilbert Transform of the difference signal in thefrequency domain.
 10. A method for detecting a vibrating blade of arotating rotor in an operating turbine having an acoustic sensorpositioned on a stationary member with respect to said rotor to receivesound waves emanating from said vibrating blade of said rotor as saidblade rotates about said rotor axis and to provide an acoustic signalfrom said received sound waves,said acoustic sensor positioned withrespect to said rotor so that said blade approaches and departs fromsaid acoustic sensor in the course of one rotation of said rotor aboutsaid rotor axis thereby imparting a Doppler effect to said receivedsound waves comprising the steps of: obtaining a reference signalindicative of rotor position at least once each time said rotorcompletes a revolution about said rotor axis and for determining theangular velocity of said rotor, sampling said acoustic signal to obtainsamples as a function of rotor position as said rotor completes aplurality of revolutions at a first and at a second angular velocity ofsaid rotor, averaging said samples obtained at respective rotorpositions of said rotor revolving at said first angular velocity andrevolving at said second angular velocity, subtracting the averagedsamples obtained at respective rotor positions of said rotor revolvingat said first and at said second angular velocity to provide adifference signal at respective rotor positions of said rotor wherebyorder-related background noise due to other blades having nonuniformityin angular position on the rotor is removed, and comparing the amplitudeof said difference signal at respective rotor positions of said rotorwith a threshold value whereby amplitudes above said threshold value areindicative of said vibrating blade.
 11. The method of claim 10, whereinsaid step of obtaining includes the step of sensing a reference signalfrom the shaft of the rotor.
 12. The method of claim 10, wherein saidstep of sampling includes the step of sampling at said first and secondangular velocity where said first and second angular velocity are spacedapart by at least one revolution per minute.
 13. The method of claim 10,wherein said step of averaging includes the step of averaging samplesover at least one thousand revolutions of said rotor.
 14. The method ofclaim 10, wherein said step of comparing includes the first step ofdetermining the rotor position at the peak amplitude of said differencesignal at times the difference signal exceeds the threshold value. 15.The method of claim 14, wherein said first step of determining includesthe second step of determining the frequency of said difference signalat said peak amplitude.
 16. The method of claim 15, wherein said secondstep of determining includes the third step of determining theinstantaneous phase of said difference signal at said peak amplitude.17. The method of claim 16, wherein said second step of determiningincludes the step of differentiating the instantaneous phase of saiddifference signal.
 18. The method of claim 14, wherein said first stepof determining includes the second step of determining the differencesignal in the frequency domain and the third step of determining theHilbert Transform of the difference signal in the frequency domain. 19.An apparatus for detecting a vibrating blade of a rotating rotor in anoperating turbine comprising:first and second acoustic sensorspositioned apart by a predetermined angle of rotation of said rotor on astationary member with respect to said rotor to receive sound wavesemanating from said vibrating blade of said rotor as said blade rotatesabout said rotor axis and to provide first and second acoustic signalsfrom said received sound waves, said first and second acoustic sensorspositioned with respect to said rotor so that said blade approaches anddeparts from said first and second acoustic sensors in the course of onerotation of said rotor about said rotor axis thereby imparting a Dopplereffect to said received sound waves, first means for obtaining areference signal indicative of rotor position at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, second means forsampling said first and second acoustic signals from said first andsecond acoustic sensors respectively to obtain samples as a function ofrespective rotor positions as said rotor completes a plurality ofrevolutions at a first and at a second angular velocity of said rotor,third means for averaging said samples of each of said first and secondsignals obtained at respective rotor positions of said rotor revolvingat said first angular velocity and revolving at said second angularvelocity, fourth means for subtracting the averaged samples of saidfirst signal obtained at respective rotor positions of said rotorrevolving at said first and at said second angular velocity to provide afirst difference signal at respective rotor positions of said rotorwhereby order-related background noise due to other blades havingnonuniformity in angular position on the rotor is removed, fifth meansfor subtracting the amplitudes of averaged samples of said second signalobtained at respective rotor positions of said rotor revolving at saidfirst and at said second angular velocity to provide a second differencesignal at respective rotor positions of said rotor whereby order relatedbackground noise due to other blades having nonuniformity in angularposition on the rotor is reduced, sixth means for time shifting saidfirst difference signal with respect to said second difference signal sothat said first difference signal corresponds to the same respectiveposition on the rotor as said second difference signal, seventh meansfor subtracting said first and second difference signals to provide adifference-difference signal whereby order related background noise isfurther reduced, and eighth means for comparing the amplitude of saiddifference-difference signal at respective rotor positions of said rotorwith a threshold value whereby amplitudes above said threshold value areindicative of said vibrating blades.
 20. The apparatus of claim 19,further including ninth means for attenuating said first differencesignal so that the amplitudes of said first and second differencesignals are optimized for reducing order-related background noise attimes they are subtracted.
 21. The apparatus of claim 19, wherein saidfirst means includes ninth means for obtaining a reference signal fromthe shaft of the rotor.
 22. The apparatus of claim 19, wherein saidsecond means for sampling includes ninth means for sampling at saidfirst and second angular velocity where said first and second angularvelocity are spaced apart by at least one revolution per minute.
 23. Theapparatus of claim 19, wherein said third means for averaging includesninth means for averaging samples over at least one thousand revolutionsof said rotor.
 24. The apparatus of claim 19, wherein said eighth meansincludes ninth means for determining the rotor position at the peakamplitude of said difference-difference signal at times thedifference-difference signal exceeds the threshold value.
 25. Theapparatus of claim 24, wherein said ninth means includes tenth means fordetermining the frequency of said difference-difference signal at saidpeak amplitude.
 26. The apparatus of claim 25, wherein said tenth meansincludes eleventh means for determining the instantaneous phase of saiddifference-difference signal at said peak amplitude.
 27. The apparatusof claim 26, wherein said tenth means include twelfth means fordifferentiating the instantaneous phase of said difference-differencesignal.
 28. The apparatus of claim 24, wherein said ninth means includestenth means for obtaining the difference-difference signal in thefrequency domain and eleventh means for obtaining the Hilbert Transformof the difference-difference signal in the frequency domain.
 29. Amethod for detecting a vibrating blade of a rotating rotor in anoperating turbine having:first and second acoustic sensors positionedapart by a predetermined angle of rotation of said rotor on a stationarymember with respect to said rotor to receive sound waves emanating fromsaid vibrating blade of said rotor as said blade rotates about saidrotor axis and to provide first and second acoustic signals from saidreceived sound waves, said first and second acoustic sensors positionedwith respect to said rotor so that said blade approaches and departsfrom said first and second acoustic sensors in the course of onerotation of said rotor about said rotor axis thereby imparting a Dopplereffect to said received sound waves comprising the steps of: obtaining areference signal indicative of rotor position at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, sampling said first andsecond acoustic signals from said first and second acoustic sensorsrespectively to obtain samples as a function of respective rotorpositions as said rotor completes a plurality of revolutions at a firstand at a second angular velocity of said rotor, averaging said samplesof each of said first and second signals obtained at respective rotorpositions of said rotor revolving at said first angular velocity andrevolving at said second angular velocity, subtracting the averagedsamples of said first signal obtained at respective rotor positions ofsaid rotor revolving at said first and at said second angular velocityto provide a first difference signal at respective rotor positions ofsaid rotor whereby order-related background noise due to other bladeshaving nonuniformity in angular position on the rotor is removed,subtracting the amplitudes of averaged samples of said second signalobtained at respective rotor positions of said rotor revolving at saidfirst and at said second angular velocity to provide a second differencesignal at respective rotor positions of said rotor whereby order relatedbackground noise due to other blades having nonuniformity in angularposition on the rotor is reduced, time shifting said first differencesignal with respect to said second difference signal so that said firstdifference signal corresponds to the same respective position on therotor as said second difference signal, subtracting said first andsecond difference signals to provide a difference-difference signalwhereby order related background noise is further reduced, and comparingthe amplitude of said difference-difference signal at respective rotorpositions of said rotor with a threshold value whereby amplitudes abovesaid threshold value are indicative of said vibrating blades.
 30. Themethod of claim 29, further including the steps of attenuating said fistdifference signal so that the amplitudes of said first and seconddifference signals are optimized for reducing order-related backgroundnoise at times they are subtracted.
 31. The method of claim 29, whereinsaid step of obtaining includes the step of receiving a reference signalfrom the shaft of the rotor.
 32. The method of claim 29, wherein saidstep of sampling includes the step of further sampling at said first andsecond angular velocity where said first and second angular velocity arespaced apart by at least one revolution per minute.
 33. The method ofclaim 29, wherein said step of averaging includes the step of furtheraveraging samples over at least one thousand revolutions of said rotor.34. The method of claim 29, wherein said step of comparing includes thestep of determining the rotor position at the peak amplitude of saiddifference-difference signal at times the difference-difference signalexceeds the threshold value.
 35. The method of claim 34, wherein saidstep of determining includes the step of further determining thefrequency of said difference-difference signal at said peak amplitude.36. The method of claim 35, wherein said step of further obtainingincludes the step of additionally determining the instantaneous phase ofsaid difference-difference signal at said peak amplitude.
 37. The methodof claim 36, wherein said step of further obtaining includes the step ofdifferentiating the instantaneous phase of said difference-differencesignal.
 38. The method of claim 34, wherein said step of determiningincludes the step of further obtaining the difference-difference signalin the frequency domain and eleventh means for obtaining the HilbertTransform of the difference-difference signal in the frequency domain.39. An apparatus for detecting a non order-related vibrating blade of arotating rotor in an operating turbine comprising:an acoustic sensorpositioned on a stationary member with respect to said rotor to receivesound waves emanating from said vibrating blade of said rotor as saidblade rotates about said rotor axis and to provide an acoustic signalfrom said receive sound waves, said acoustic sensor positioned withrespect to said rotor so that said blade approaches and departs fromsaid acoustic sensor in the course of one rotation of said rotor aboutsaid rotor axis thereby imparting a Doppler effect to said receivedsound waves, first means for obtaining a reference signal indicative ofrotor positions at least once each time said rotor completes arevolution about said rotor axis and for determining the angularvelocity of said rotor, second means for sampling said acoustic signalto obtain samples as a function of rotor position as said rotorcompletes a plurality of revolutions at a plurality of angularvelocities of said rotor, third means for averaging said samplesobtained at respective rotor positions of said rotor revolving at eachangular velocity of said plurality of angular velocities and for storingthe averaged samples, fourth means for subtracting the averaged samplesobtained at respective rotor positions of said rotor revolving at eachangular velocity of said plurality of angular velocities from individualsamples obtained at respective rotor positions of said rotor revolvingat each angular velocity of said plurality of angular velocities toprovide a difference signal sample at respective rotor positions of saidrotor revolving at said plurality of angular velocities whereby nonorder-related background noise due to flow noise and non order-relatedvibrating blades is extracted, fifth means for determining the root meansquare (RMS) of a plurality of difference signal samples at respectiverotor positions of said rotor revolving at each angular velocity of saidplurality of angular velocities to form a root mean square differencesample at respective rotor positions of said rotor revolving at saidplurality of angular velocities, sixth means for determining the rootmeans square (RMS) of said root means square difference samples atrespective rotor positions of said rotor revolving at each angularvelocity of said plurality of velocities to form a root mean squarerunning speed signal, seventh means for subtracting the amplitude ofsaid root mean square running speed signal at each respective angularvelocity from the amplitude of said root mean square difference samplesat the same corresponding angular velocity to form reduced root meansquare difference samples at respective rotor positions and angularvelocities, eighth means for averaging over several revolutions saidreduced root mean square difference samples at respective rotorpositions of said rotor revolving at respective angular velocities, andninth means for comparing said averaged and reduced root mean squaredifference samples at respective rotor positions of said rotor revolvingat respective angular velocities with a threshold value wherebyamplitudes above said threshold value are indicative of said nonorder-related vibrating blade.
 40. The apparatus of claim 39, furtherincluding tenth means for providing torsional vibration to said rotor ata predetermined frequency whereby small corresponding vibrations tocertain turbine blades are observed for turbine blades having a bladeresonance at said frequency.
 41. The apparatus of claim 40, wherein saidtenth means includes an exciter coupled to the generator sharing thesame rotor shaft.
 42. The apparatus of claim 41, wherein said exciter iscoupled to the field windings of said generator.
 43. A method fordetecting a non order-related vibrating blade of a rotating rotor in anoperating turbine having:an acoustic sensor positioned on a stationarymember with respect to said rotor to receive sound waves emanating fromsaid vibrating blade of said rotor as said blade rotates about saidrotor axis and to provide an acoustic signal from said receive soundwaves, said acoustic sensor positioned with respect to said rotor sothat said blade approaches and departs from said acoustic sensor in thecourse of one rotation of said rotor about said rotor axis therebyimparting a Doppler effect to said received sound waves comprising thesteps of: first obtaining a reference signal indicative of rotorpositions at least once each time said rotor completes a revolutionabout said rotor axis and for determining the angular velocity of saidrotor, second sampling said acoustic signal to obtain samples is afunction of rotor position as said rotor completes a plurality ofrevolutions at a plurality of angular velocities of said rotor, thirdaveraging said samples obtained at respective rotor positions of saidrotor revolving at each angular velocity of said plurality of angularvelocities and for storing the averaged samples, fourth subtracting theaveraged samples obtained at respective rotor positions of said rotorrevolving at each angular velocity of said plurality of angularvelocities from individual samples obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities to provide a difference signal sample atrespective rotor positions of said rotor revolving at said plurality ofangular velocities whereby non order-related background noise due toflow noise and non order-related vibrating blades is extracted, fifthdetermining the root mean square (RMS) of a plurality of differencesignal samples at respective rotor positions of said rotor revolving ateach angular velocity of said plurality of angular velocities to form aroot mean square difference sample at respective rotor positions of saidrotor revolving at said plurality of angular velocities, sixthdetermining the root means square (RMS) of said root means squaredifference samples at respective rotor positions of said rotor revolvingat each angular velocity of said plurality of velocities to form a rootmean square running speed signal, seventh subtracting the amplitude ofsaid root mean square running speed signal at each respective angularvelocity from the amplitude of said root mean square difference samplesat the same corresponding angular velocity to form reduced root meansquare difference samples at respective rotor positions and angularvelocities, eighth averaging over several revolutions said reduced rootmean square difference samples at respective rotor positions of saidrotor revolving at respective angular velocities, and ninth comparingsaid averaged and reduced root mean square difference samples atrespective rotor positions of said rotor revolving at respective angularvelocities with a threshold value whereby amplitudes above saidthreshold value are indicative of said non order-related vibratingblade.
 44. The method of claim 43, further including tenth providingtorsional vibration to said rotor at a predetermined frequency wherebysmall corresponding vibration to certain turbine blades are observed forturbine blades having a blade resonance at said frequency.
 45. Themethod of claim 44, wherein said tenth step of providing includescoupling an exciter to the generator sharing the same rotor shaft. 46.The method of claim 45, wherein said step of coupling an exciterincludes the step of coupling said exciter to the field windings of saidgenerator.
 47. An apparatus for detecting an aerodynamic event in anoperating turbine comprising:an acoustic sensor positioned on astationary member with respect to said rotor of said turbine to receivesound waves emanating from and near the blades of a blade row of saidrotor as said rotor rotates about said rotor axis to provide an acousticsignal from said received sound waves, first means for obtaining areference signal indicative of rotor positions at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, second means forsampling said acoustic signal to obtain samples as a function of rotorposition as said rotor completes a plurality of revolutions at aplurality of angular velocities of said rotor, third means for averagingsaid samples obtained at respective rotor positions of said rotorrevolving at each angular velocity of said plurality of angularvelocities and for storing the averaged samples, fourth means forsubtracting the amplitudes of averaged samples obtained at respectiverotor positions of said rotor revolving at each angular velocity of saidplurality of angular velocities from individual samples obtained atrespective rotor positions of said rotor revolving at each angularvelocity of said plurality of angular velocities to provide a differencesignal sample at respective rotor positions of said rotor revolving atsaid plurality of angular velocities whereby non order-relatedaerodynamic events and background noise due to flow noise and bladevibration is extracted, and to provide an output signal at times saiddifference signal sample exceeds said predetermined value indicative ofan aerodynamic event.
 48. A method for detecting an aerodynamic event inan operating turbine havingan acoustic sensor positioned on a stationarymember with respect to said rotor of said turbine to receive sound wavesemanating from and near the blades of a blade row of said rotor as saidrotor rotates about said rotor axis to provide an acoustic signal fromsaid received sound waves comprising the steps of: first obtaining areference signal indicative of rotor positions at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, second sampling saidacoustic signal to obtain samples as a function of rotor position assaid rotor completes a plurality of revolutions at a plurality ofangular velocities of said rotor, third averaging said samples obtainedat respective rotor positions of said rotor revolving at each angularvelocity of said plurality of angular velocities and for storing theaveraged samples, fourth subtracting the amplitudes of averaged samplesobtained at respective rotor positions of said rotor revolving at eachangular velocity of said plurality of angular velocities from individualsamples obtained at respective rotor positions of said rotor revolvingat each angular velocity of said plurality of angular velocities toprovide a difference signal sample at respective rotor positions of saidrotor revolving at said plurality of angular velocities whereby nonorder-related aerodynamic events and background noise due to flow noiseand blade vibration is extracted, and to provide an output signal attimes said difference signal sample exceeds said predetermined valueindicative of an aerodynamic event.
 49. An apparatus for detecting anaerodynamic event of condensation shock in an operating turbinecomprising:a first and second acoustic sensor positioned on a stationarymember with respect to the rotor of said turbine to receive sound wavesemanating from and near the blades of a blade row of said rotor as saidrotor rotates about said rotor axis to provide a first and secondacoustic signal from said received sound waves, first means forobtaining a reference signal indicative of rotor positions at least onceeach time said rotor completes a revolution about said rotor axis andfor determining the angular velocity of said rotor, second means forsampling said first and second acoustic signals to obtain samples ofsaid first and second signals respectively as a function of rotorposition as said rotor completes a plurality of revolutions at aplurality of angular velocities of said rotor, third means for averagingthe said samples of said first and second signals obtained at respectiverotor positions of said rotor revolving at each angular velocity of saidplurality of angular velocities and for storing the averaged samples ofsaid first and second signals, fourth means for subtracting the averagedsamples of said first and second signals obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities from individual samples obtained atrespective rotor positions of said rotor revolving at each angularvelocity of said plurality of angular velocities to provide first andsecond difference signal sample of said first and second signals atrespective rotor positions of said rotor revolving at said plurality ofangular velocities whereby non order-related aerodynamic events andbackground noise due to flow noise and blade vibration is extracted, andcomparing the amplitude of said first and second difference signalsamples of said first and second signals with respective first andsecond predetermined values, said first and second predetermined valuesset above said background noise due to flow noise and non order-relatedblade vibration to provide a first and second output signal at times theamplitude of said first and second difference signal sample exceeds saidrespective first and second predetermined value, means for comparing thetime difference between said first and second output signals whereby atime difference below a third predetermined value is indicative of anaerodynamic event of condensation shock in said turbine.
 50. A methodfor detecting an aerodynamic event of condensation shock in an operatingturbine havinga first and second acoustic sensor positioned on astationary member with respect to the rotor of said turbine to receivesound waves emanating from and near the blades of a blade row of saidrotor as said rotor rotates about said rotor axis to provide a first andsecond acoustic signal from said received sound waves comprising thesteps of: first obtaining a reference signal indicative of rotorpositions at least once each time said rotor completes a revolutionabout said rotor axis and for determining the angular velocity of saidrotor, second sampling said first and second acoustic signals to obtainsamples of said first and second signals respectively as a function ofrotor position as said rotor completes a plurality of revolutions at aplurality of angular velocities of said rotor, third averaging the saidsamples of said first and second signals obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities and for storing the averaged samples ofsaid first and second signals, fourth subtracting said averaged samplesof said first and second signals obtained at respective rotor positionsof said rotor revolving at each angular velocity of said plurality ofangular velocities from individual samples obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities to provide first and second differencesignal sample of said first and second signals at respective rotorpositions of said rotor revolving at said plurality of angularvelocities whereby non order-related aerodynamic events and backgroundnoise due to flow noise and blade vibration is extracted, fifthcomparing the amplitude of said first and second difference signalsamples of said first and second signals with respective first andsecond predetermined values, said first and second predetermined valuesset above said background noise cue to flow noise and non order-relatedblade vibration to provide a first and second output signal at times theamplitude of said first and second difference signal sample exceeds saidrespective first and second predetermined value, and sixth comparing thetime difference between said first and second output signals whereby atime difference below a third predetermined value is indicative of anaerodynamic event of condensation shock in said turbine.
 51. Anapparatus for detecting an aerodynamic event of rotating stall in anoperating turbine comprising:a first and second acoustic sensorpositioned on a stationary member with respect to the rotor of saidturbine to receive sound waves emanating from and near the blades of ablade row of said rotor as said rotor rotates about said rotor axis toprovide a first and second acoustic signal from said received soundwaves, first means for obtaining a reference signal indicative of rotorpositions at least once each time said rotor completes a revolutionabout said rotor axis and for determining the angular velocity of saidrotor, second means for sampling said first and second acoustic signalsto obtain samples of said first and second signals respectively as afunction of rotor position as said rotor completes a plurality ofrevolutions at a plurality of angular velocities of said rotor, thirdmeans for averaging said samples of said first and second signalsobtained at respective rotor positions of said rotor revolving at eachangular velocity of said plurality of angular velocities and for storingthe averaged samples of said first and second signals, fourth means forsubtracting the averaged samples of said first and second signalsobtained at respective rotor positions of said rotor revolving at eachangular velocity of said plurality of angular velocities from individualsamples obtained at respective rotor positions of said rotor revolvingat each angular velocity of said plurality of angular velocities toprovide first and second difference signal sample of said first andsecond signals at respective rotor positions of said rotor revolving atsaid plurality of angular velocities whereby non order-relatedaerodynamic events and background noise due to flow noise and bladevibration is extracted, and fifth means for comparing the amplitude ofsaid first and second difference signal samples of said first and secondsignals with respective first and second predetermined values, saidfirst and second predetermined values set above said background noisedue to flow noise and non order-related blade vibration to provide afirst and second output signal at times the amplitude of said first andsecond difference signal sample exceeds said respective first and secondpredetermined value, means for fifth means for comparing the timedifference between said first and second output signals whereby a timedifference below a third predetermined value is indicative of anaerodynamic event of condensation shock in said turbine.
 52. A methodfor detecting an aerodynamic event of rotating stall in an operatingturbine havinga first and second acoustic sensor positioned on astationary member with respect to the rotor of said turbine to receivesound waves emanating from and near the blades of a blade row of saidrotor as said rotor rotates about said rotor axis to provide a first andsecond acoustic signal from said received sound waves comprising thesteps of: first obtaining a reference signal indicative of rotorpositions at least once each time said rotor completes a revolutionabout said rotor axis and for determining the angular velocity of saidrotor, second sampling said first and second acoustic signals to obtainsamples of said first and second signals respectively as a function ofrotor position as said rotor completes a plurality of revolutions at aplurality of angular velocities of said rotor, third averaging saidsamples of said first and second signals obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities and for storing the averaged samples ofsaid first and second signals, fourth subtracting the averaged samplesof said first and second signals obtained at respective rotor positionsof said rotor revolving at each angular velocity of said plurality ofangular velocities from individual samples obtained at respective rotorpositions of said rotor revolving at each angular velocity of saidplurality of angular velocities to provide first and second differencesignal sample of said first and second signals at respective rotorpositions of said rotor revolving at said plurality of angularvelocities whereby non order-related aerodynamic events and backgroundnoise due to flow noise and blade vibration is extracted, fifthcomparing the amplitude of said first and second difference signalsamples of said first and second signals with respective first andsecond predetermined values, said first and second predetermined valuesset above said background noise due to flow noise and non order-relatedblade vibration to provide a first and second output signal at times theamplitude of said first and second difference signal sample exceeds saidrespective first and second predetermined value, and sixth comparing thetime difference between said first and second output signals whereby atime difference below a third predetermined value is indicative of anaerodynamic event of rotating stall in a blade row in said turbine. 53.An apparatus for detecting differential nozzle wear between two or morenozzle sections in a high pressure turbine comprising:a first and secondacoustic sensor positioned downstream of a rotating blade row anddownstream of respective first and second nozzle sections of a turbineto receive sound waves emanating from said blade row and individualvibrating blades of said blade row rotating as part of a rotor about arotor axis to provide an acoustic signal from said received sound waves,first means for obtaining a reference signal indicative of rotorposition at least once each time said rotor completes a revolution aboutsaid rotor axis and for determining the angular velocity of said rotor,second means for sampling said first and second acoustic signals toobtain first and second samples as a function of rotor position as saidrotor completes a plurality of revolutions at one of a plurality ofangular velocities of said rotor, third means for averaging said firstand second samples of said first and second acoustic signals obtained atrespective rotor positions of said rotor revolving at said angularvelocity, fourth means for phase shifting said second samples of saidsecond acoustic signal whereby said first samples of said first acousticsignal and said second samples of said second acoustic signal correspondto the same place on the rotor, and fifth means for subtracting saidfirst samples of said first acoustic signal from said second samples ofsaid second acoustic signal to provide a difference signal indicative ofnozzle wear between said first and second nozzles.
 54. A method fordetecting differential nozzle wear between two or more nozzle sectionsin a high pressure turbine having:a first and second acoustic sensorpositioned downstream of a rotating blade row and downstream ofrespective first and second nozzle sections of a turbine to receivesound waves emanating from said blade row and individual vibratingblades of said blade row rotating as part of a rotor about a rotor axisto provide an acoustic signal from said received sound waves comprisingthe steps of first obtaining a reference signal indicative of rotorposition at least once each time said rotor completes a revolution aboutsaid rotor axis and for determining the angular velocity of said rotor,second sampling said first and second acoustic signals to obtain firstand second samples as a function of rotor position as said rotorcompletes a plurality of revolutions at one of a plurality of angularvelocities of said rotor, third averaging said first and second samplesof said first and second acoustic signals obtained at respective rotorpositions of said rotor revolving at said angular velocity, fourth phaseshifting said second samples of said second acoustic signal whereby saidfirst samples of said first acoustic signal and said second samples ofsaid second acoustic signal correspond to the same place on the rotor,and fifth subtracting said first samples of said first acoustic signalfrom said second samples of said second acoustic signal to provide adifference signal indicative of nozzle wear between said first andsecond nozzles.
 55. Apparatus for measuring the order-related torsionalresonant shaft vibration of a rotor shaft in an operating turbinecomprising:an acoustic sensor positioned on a stationary member withrespect to said rotor to receive sound waves emanating from vibratingblades of said rotor as said blades rotate about said rotor axis and toprovide an acoustic signal from said received soundwaves, said acousticsensor positioned with respect to said rotor so that said bladesapproach and depart from said acoustic sensor in the course of onerotation of said rotor about said rotor axis thereby imparting a Dopplereffect to said received sound waves, first means for obtaining areference signal indicative of rotor position at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, second means forsampling said acoustic signal to obtain samples as a function of rotorposition as said rotor completes a plurality of revolutions at a firstand at a second angular velocities of said rotor, third means foraveraging said samples of said acoustic signal obtained at respectiverotor positions of said rotor revolving at said first angular velocityand revolving at said second angular velocity, fourth means forsubtracting the averaged samples obtained at respective rotor positionsof said rotor revolving at said first and at said second angularvelocity to provide a difference signal at respective rotor positions ofsaid rotor whereby order-related background noise due to other bladeshaving nonuniformity in angular position on the rotor is removed, andfifth means for detecting a sine wave modulation in the amplitude ofsaid difference signal as a function of one revolution of said rotorshaft and for providing a signal indicative of torsional resonant shaftvibration of said rotor shaft at times said sine wave modulation isdetected.
 56. The apparatus of claim 55, wherein said fifth meansincludes means for taking the Hilbert Transform of said differencesignal.
 57. A method for measuring the order-related torsional resonantshaft vibration of a rotor shaft in an operating turbine havinganacoustic sensor positioned on a stationary member with respect to saidrotor to receive sound waves emanating from vibrating blades of saidrotor as said blades rotate about said rotor axis and to provide anacoustic signal from said received soundwaves, said acoustic sensorpositioned with respect to said rotor so that said blades approach anddepart from said acoustic sensor in the course of one rotation of saidrotor about said rotor axis thereby imparting a Doppler effect to saidreceived sound waves comprising the steps of: first obtaining areference signal indicative of rotor position at least once each timesaid rotor completes a revolution about said rotor axis and fordetermining the angular velocity of said rotor, second sampling saidacoustic signal to obtain samples as a function of rotor position assaid rotor completes a plurality of revolutions at a first and at asecond angular velocities of said rotor, third averaging said samples ofsaid acoustic signal obtained at respective rotor positions of saidrotor revolving at said first angular velocity and revolving at saidsecond angular velocity, fourth subtracting said averaged samplesobtained at respective rotor positions of said rotor revolving at saidfirst and at said second angular velocity to provide a difference signalat respective rotor positions of said rotor whereby order-relatedbackground noise due to other blades having nonuniformity in angularposition on the rotor is removed, and fifth detecting a sine wavemodulation in the amplitude of said difference signal as a function ofone revolution of said rotor shaft and for providing a signal indicativeof torsional resonant shaft vibration of said rotor shaft at times saidsine wave modulation is detected.
 58. The apparatus of claim 57, whereinsaid step of fifth detecting includes the step of sixth taking theHilbert Transform of said difference signal.
 59. In an apparatus fordetecting vibrations in a turbine blade, wherein at least one acousticsensor is positioned in juxtaposition to the blade, thereby obtaining anacoustic signal from the sensor, and wherein spurious noise mayinterfere with the acoustic signal and its signal-to-noise ratio, theimprovement which comprises means for obtaining a difference Dopplereffect of the acoustic signal, thereby substantially improving thesignal-to-noise ratio of the acoustic signal for substantially improveddetection of turbine blade vibration.
 60. A method for detecting avibrating blade of a rotating rotor in an operating turbine having atleast one acoustic sensor positioned in juxtaposition to the blade toreceive sound waves emanating from the vibrating blade of the rotorcomprising the steps of:obtaining an acoustic signal from the at leastone sensor; obtaining a difference Doppler waveform of the signal; andcomparing the difference Doppler waveform with the sound signals suchthat the signal to noise ratio is improved and the vibrating blade maybe detected.